x-ray imaging - queen's...

Laboratory for Percutaneous Surgery (The Perk Lab) – Copyright © Queen’s University, 9/26/2017

X-ray imaging


Würzburg, November 8, 1895: Dr. Wilhelm Conrad Röntgen


Heat

=DC

Fluorescence in glass tube by cathode rays

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Glowing light in gas

http://pdg.lbl.gov/cpep/map_proj.html



Röntgen’s experiment

Heat

=DC

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Black cardboard box

Faint glowing

Barium Platinum Cyanide

50cm




What did Röntgen know and did not know?

DID KNOW• Ray-like phenomenon (named it X for “unknown” ray)• Not charged• Carries to some distance• Penetrates through regular materials• Absorption rate depends on material density• Absorption depends on material mass• Carries significant energy• Energy changes with tube voltageDID NOT KNOW• Electromagnetic wave, just like visible light• Shorter wavelength (E=h*n)• Always harmful, potentially lethal


Frau Röntgen’s hand, December, 1895


Chest X-ray, 1903


Army hospital 1915


Bucky Grid (1913)


Potter’s Grid (1920)


Collimator grid


X-ray of a hand1895

2002


••

•

Modern chest X-ray machine

Number of X-rays registered by Medicare in 1993:

207,753,747


X-ray process (in its full glory)


X-Ray dermatitis & protection1910

1914


Figure 24. An important, and adjustable, determinant of image quality in radiography is the voltage

applied across the X-ray tube by the generator. The image to the left, (a), was made at a lower voltage

(70,000 V) than (b), the one on the right (110,000V). As a result, (a) more clearly shows the two ureters,

which are carrying urine (and iodine-based contrast agent) from the kidneys to the bladder. The lower the

voltage, the better the contrast, but the greater the amount of radiation dose that is delivered to the

patient-one of many trade-offs to be considered in imaging. Courtesy of the American College of

Radiology.

Effect of tube voltage


Decay of intensity in matter


X-ray interaction with DNA


Radiation risk

• Generally, risk is the possibility (not probability) that something bad may happen

• Risk is subjective and the public’s feeling depends on the source of risk– Human made hazards are less acceptable

– Risk feels greater if comes without consent or consultation

– Accidents increase the feel of risk

– Terrorism is the supreme tool in creating extreme feeling of risk

• Radiological risk: the possibility that X-ray used in medical procedures may give rise to cancer.

• It is real, documented to happen, and objectively measurable.

• Risk = Dose * Risk-probability

• Risk-probability depends on the type of cancer & organ – how much dose over how long a time the organ tolerates before (w/ some probability) it becomes cancerous

• Yardstick: whole-body cosmic background radiation (BGR) 300 mrem /year.

• Chest X-ray: 20 mrem upon skin entry, 2 mrem upon exit

• Equivalent cancer risk:

– For Skin : Cosmic BGR = 15 X-ray shots /year

– For most internal organs: Cosmic BGR = 150 X-ray shots /year


X-ray = terror and horror


Dose escalation models

• Under perennial debate

• It has been linear accumulation model: the body never forgets radiation

• But, the body does forget radiation, we just do not know how

• How does genetic distortion caused by ionizing radiation fades out? – We do not know

• “Annual limits” for medical staff

• Dose tolerance levels are set for organs

• Sensory organs are very sensitive

• Brain, lymph nodes, bone marrow are generally sensitive

• Large differences in tolerance, even within one organ (brain)


Typical X-ray imager modelPoint source & cone beam


X-ray projection

X-ray source (point source)

Project an object onto the

detector to obtain an image

(shadow) of the object on the

detector.Object

Image

Detector


X-ray magnification

X-ray detector


beam central

Object

Shadow

SDD (source-detector distance)

SOD (source-target plane distance)

Linear magnification ≈

Areal magnification ≈

SDD/SOD

(SDD/SOD)2

Target plane


Loss of 3rd dimension (depth)

X-ray detector


Target ?

Shadow

From the X-ray image only, we

cannot tell the location, shape and

size of the target

Because:• Projection has no inverse

• Projection is irreversible

• Projection loses sense of

depth


Back projection (BP)

X-ray detector


Draw lines from the object’s

shadow back from detector

toward the X-ray source.

The object must sit on these

lines somewhere...


Rotational X-ray & coordinate system

Source

X-ray

detector

X-ray

coord

system

Detector

coord

system

Beam

Central


Typical mobile rotational X-ray (C-arm)


X-ray reconstruction of small target

• Take two or more x-ray shots in different X-ray

poses

• Keep the patient stationary!

• Find centers of target images (T1, T2., … Tn.)

• Write up the equations of all BP lines

• Compute intersection of all BP lines

S1S2

T1

T2

T

BP1BP2


Why BP lines do not intersect?

• BP lines in space never intersect but can come close

• Some sources of error :

– Target Localization Error in detector

– Target are too large - point model is wrong

– Image warping

– Mechanical imperfections

• SSD, SAD, Detector center not known accurately

• Rotation angles not known accurately

• Patient moves between shots

• X-ray source/detector motion between shots

– Axis wobbling

– Mechanical deformation

– Accidental motion on rubber wheels


Target correspondence problemSmall similar targets

Which belongs to which?

Brute force solution: assign them in all possible

combinations; compute reconstruction; compute

reconstruction error – the error is the smallest when the

correct correspondence.

Works for small number of targets that are quite

distantly situated. (NP hard problem, exponential

blow.) Dog shot with 100+

BB gun slugs


Epipolar constraint to solve correspondance

S1S2

G

B

G2

B2

B1

G1

Thought experiment: replace S2-G2 line with a thin

“wire”, and use S1 source to project the wire onto D1

detector. The result is the so called epipolar line.

Since B lies somewhere on the “wire”, B1 must lie on

the projection image of the wire (epipolar line). G1 is

probably not on the epipolar line – we can use this to

positively match G1 and G2.

Epipolar line


When hell breaks loose…

Radioactive seed implants in the prostate

brachytherapy: Imagine over 100 rice grains in a

golf ball


X-ray reconstruction of large solid target• We assume the target to be a dense object

• Take many x-ray shots

• We weep the object (patient) stationary

• Reconstruct the approximate center of the

target: • Find centers of target images (T1, T2., … Tn.)

• Write up the equations of all BP lines

• Compute intersection of all BP lines

• Next, we reconstruct the shape as well as we

can…

S1S2

T1

T2

T

BP1BP2

T1

Step-1


X-ray reconstruction of large solid target• We put a super-cube around target’s centre

that encompasses the target

• We subdivide the cube to many tiny-tiny

cubelets (voxels)

• We forward project each voxel onto ceach

detector. If the shadow of the voxel falls

outside the target’s countour, the voxel does

not belong to the target – RED cubelet

• If in all images, the voxel’s shadow falls inside

the target, the voxel belongs to the target –

GREEN voxel

• We repeat this for each voxel…

S1S2

T1

Step-2


X-ray reconstruction of large solid target• Having repeated the test for all voxels in the

super-cube, we and up with a pile of green

voxels representing the inside of the target

surrounded by red voxel outside the target.

• We may connect the voxels into a solid object,

if need to.

• We can use convex hull – but that obliterates

all concavities

• From large number of images, we can

approximately reconstruct a shape.

• We cannot reconstruct dimples and holes.

• But some concave shapes like a kidney can

be reconstructed.

• We may not want to reconstruct a detail that

we cannot treat anyway.

S1S2

T1

Step-3


X-ray reconstruction of large solid targetOPTIMIZATION:

• Reconstruction quality and time increase

with

• Smaller voxel size

• Larger number of X-ray shots

• Reduce number of “empty” voxels by:

• Making the super-cube the smallest

• Use the tightest fitting super sphere

S1S2

T1

Step-4


Delay between shot and image


Real-time X-ray = fluoroscopy


Edison with his fluoroscope, 1896


The first commercial fluoroscope


X-ray + Television = Fluoroscopy


X-ray image intensifier tube


Mobile C-arm fluoroscopes


Some fluoroscopy images


Image warping

Courtesy of Yao & Taylor


Flat panel detectors


Flat panel C-arm fluoroscope


Summary: Pros and cons of X-ray

• Pros:

– Simple

– Inexpensive

– Excellent bone contrast

• Cons:

– Harmful dose to patient

– Loss of shape and depth of objects

– Poor soft tissue contrast

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